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  2. Rhombus - Wikipedia

    en.wikipedia.org/wiki/Rhombus

    Using congruent triangles, one can prove that the rhombus is symmetric across each of these diagonals. It follows that any rhombus has the following properties: Opposite angles of a rhombus have equal measure. The two diagonals of a rhombus are perpendicular; that is, a rhombus is an orthodiagonal quadrilateral. Its diagonals bisect opposite ...

  3. Equidiagonal quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Equidiagonal_quadrilateral

    In Euclidean geometry, an equidiagonal quadrilateral is a convex quadrilateral whose two diagonals have equal length. Equidiagonal quadrilaterals were important in ancient Indian mathematics , where quadrilaterals were classified first according to whether they were equidiagonal and then into more specialized types.

  4. Square - Wikipedia

    en.wikipedia.org/wiki/Square

    A rhombus with all angles equal; A parallelogram with one right vertex angle and two adjacent equal sides; A quadrilateral with four equal sides and four right angles; A quadrilateral where the diagonals are equal, and are the perpendicular bisectors of each other (i.e., a rhombus with equal diagonals)

  5. Golden ratio - Wikipedia

    en.wikipedia.org/wiki/Golden_ratio

    All side lengths are equal, but the ratio of the length of sides to the short diagonal in the thin rhombus equals ⁠: ⁠, as does the ratio of the sides of to the long diagonal of the thick rhombus. As with the kite and dart tiling, the areas of the two rhombi are in the golden ratio to each other.

  6. Difference of two squares - Wikipedia

    en.wikipedia.org/wiki/Difference_of_two_squares

    This follows from the left side of the equation being equal to zero, requiring the right side to equal zero as well, and so the vector sum of a + b (the long diagonal of the rhombus) dotted with the vector difference a - b (the short diagonal of the rhombus) must equal zero, which indicates the diagonals are perpendicular.

  7. Quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Quadrilateral

    Isosceles trapezium (UK) or isosceles trapezoid (US): one pair of opposite sides are parallel and the base angles are equal in measure. Alternative definitions are a quadrilateral with an axis of symmetry bisecting one pair of opposite sides, or a trapezoid with diagonals of equal length. Parallelogram: a quadrilateral with two pairs of ...

  8. Diagonal - Wikipedia

    en.wikipedia.org/wiki/Diagonal

    The diagonals of a cube with side length 1. AC' (shown in blue) is a space diagonal with length , while AC (shown in red) is a face diagonal and has length .. In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.

  9. Parallelogram law - Wikipedia

    en.wikipedia.org/wiki/Parallelogram_law

    For the general quadrilateral (with four sides not necessarily equal) Euler's quadrilateral theorem states + + + = + +, where is the length of the line segment joining the midpoints of the diagonals. It can be seen from the diagram that x = 0 {\displaystyle x=0} for a parallelogram, and so the general formula simplifies to the parallelogram law.

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